1. Field of the Invention
The present invention relates to an image processing apparatus which reproduces a full-color image by converting multilevel image data obtained by color separation into a halftone image for each color and then superimposing the converted halftone images on one another.
2. Description of the Related Art
The technique of dithering is widely employed as a technique for binarization or digitization in tone reproduction using a halftone screen. In dithering, matrices comprising a plurality of pixels are arranged at regular intervals to form a screen structure. The ON/OFF status of each of the pixels in the matrix is determined by comparing input signals with a conversion table, designated as a threshold matrix, a dither matrix, or the like, describing relationship between output of the pixel and an input image signal. Then, several adjoining pixels are switched between ON and OFF to generate halftone dots, and tone reproduction is carried out according to the sizes of the generated halftone dots. In color reproduction, by changing screen angles on a color basis, color variations due to expansion or contraction or variations in the positions of printing plates are suppressed by using a different screen angle for each color. However, interference of the screens having the different screen angles produces a visible low-frequency moiré.
In order to conduct an analysis of problems associated with spatial frequencies resulting from such halftone dot structures, basis vectors as described by A. Rosenfeld, A. C. Kak in Chapter 4 of “Digital Picture Processing”, Academic Press 1982 are defined for halftone dot patterns as shown in FIG. 1. An example shown in FIG. 1 represents a screen set consisting of screens for M (magenta), C (cyan), and K (black) preferentially allocated at screen angles in approximately 30 degree intervals (M at 74°, C at +16°, K at +45°) and a screen for Y (yellow) subsequently allocated at a screen angle of 0°, which is commonly used in a printing field. The example of FIG. 1 shows that a dot pattern in each color screen is an orthogonal screen. In FIG. 1, the placement of adjacent 2×2 halftone dots 100, 102, 104, and 106, and basis vectors Y1, Y2, K1, K2, M1, M2, C1, and C2 corresponding to the halftone dots are depicted. For example, basis vectors Y1 and Y2 of Y are vectors extending from a halftone dot 100-0 to adjacent screen dots 100-1 and 100-2 in the halftone dot structure of the Y screen, respectively.
From the basis vectors, spatial frequency spectra in the halftone dot structure can be defined. Writing as a general formula, reciprocal basis vectors w1 and w2, which satisfy the relationship in the following equations:ri·wj=0 (where i≠j and i, j is 1 or 2) and ri·wj=1 (where i=j),are defined for basis vectors r1 and r2, respectively. Considering the reciprocal basis vectors w1 and w2 as position vectors starting from the origin of a spatial frequency plane, the end points of reciprocal basis vectors w1 and w2 represent spatial frequency spectra in each direction. Detailed explanation about the basis vectors and the spatial frequency spectra is provided in Chapter 4 of “Digital Picture Processing” The reciprocal basis vectors described in Chapter 4 of “Digital Picture Processing” are hereafter referred to as “screen vectors” relative to a halftone screen.
FIG. 2 is a graphic plot of basis vectors of a 4-color screen set equivalent to the example of FIG. 1, which shows an example of approximately 165 lpi (lines per inch) designed with a resolution of 2400 dpi (dots per inch). In FIG. 2, the width of squares constituting a grid corresponds to 2 pixels at 2400 dpi. FIG. 3 shows spatial frequency spectra derived from the basis vectors of the 4-color screen set, which are separately plotted in their respective maps as two groups of spectra, primary spectra (the spatial frequency spectra corresponding to basis vectors Y1, Y2, K1, K2, M1, M2, C1, and C2) and secondary spectra (the spatial frequency spectra corresponding to vectors represented by the sum or the difference of the basis vectors).
FIG. 4 shows screen dot patterns for colors M, C, Y, and K defined by the basis vectors of FIG. 2, and FIG. 5 shows superimposed dot patterns of the screens for the colors. Because, in the screen set corresponding to the basis vectors of FIG. 2, the screens for M, C, and K having a high contrast in monochromatic lightness are preferentially arranged at angular intervals of approximately 30 degrees, an interval between the spatial frequency spectra for the three colors is wide, i.e. approximately 84 lpi. Such a wide spectrum interval is less prone to generate moiré of a secondary color (see (3) and (4)). Regarding Y and K, the intervals between the screen vectors are wide, and thereby their tendency to generate moiré is low (see (2)). On the contrary, secondary color G (green) of Y and C and secondary color R (red) of Y and M derived from the colors, having closer screen vectors, present low-frequency moiré of 47 lpi, which results in defective image quality (see (1)). Accordingly, when the screens for Y, M, and C are superimposed, the low-frequency moiré also emerges (see (5)).
Regarding the above-described problem, when the reproduction of human skin colors is important in printing, a measure such as replacement of spatial frequency spectra between K and M is taken to prevent the secondary color moiré of R from emerging (refer to Chapter 4 in “PostScript Screening” written by Peter Fink, Adobe Press 1992). However, this measure simply interchanges the colors which cause moiré, and does not provide a solution to the underlying problem.
As another prior-art example, an orthogonal screen set obtained by arranging primary spectra of four colors M, C, Y, and K at almost equal intervals on spatial frequencies (in other words, by placing adjacent screen vectors at intervals of approximately 22.5°) is known. FIG. 6 shows basis vectors of the screen set with 2400 dpi and 170 lpi according to the above-described arrangement scheme and FIG. 7 shows spatial frequency spectra corresponding to the screen set depicted in FIG. 6 separately plotted as two groups of primary and secondary spectra. Because the processing resolution of the above example is set at 2400 dpi, completely equal allocation cannot be achieved, although frequencies of moiré between Y-C and between Y-M can be adjusted to 63 lpi and that between M-K and between C-K can be adjusted to 71 lpi. Regarding screens constituting the above screen set, dot pattern examples are shown in FIG. 8A and moiré patterns in superimposed states are shown in FIG. 8B. As can be seen from (1), (2), and (3) of FIG. 8B, noticeable low-frequency moiré does not emerge when two color screens are superimposed.
The moiré between two color screens is not a remarkable problem in the prior-art screen set represented by the basis vectors of FIG. 6. In digital image processing, however, it is impossible to allocate halftone dot patterns at completely equal intervals, which raises a problem that low-frequency moiré emerges due to remainder components of a screen frequency between three colors. Further, the prior-art screen set represented by the basis vectors of FIG. 2 also has a similar problem of the low-frequency moiré which emerges when superimposing three colors. Referring to FIG. 9, the problem of low-frequency moiré will be described below.
Relationships between the screen vectors having M, C, and K components in the screen sets of FIGS. 2 and 6 are plotted in FIG. 9 where (a) corresponds to FIG. 2 and (b) corresponds to FIG. 6. The vector representation on the left side of (a) shows screen vectors of the colors shown in FIG. 3 and the vector representation on the right side shows the same screen vectors with K1 and K2 translated so as to adjoin the tip ends of the vectors representing the screen spectra of M and C. In an analogous fashion, (b) depicts the screen spectra of FIG. 7. As shown in the circled parts of FIG. 9, the screen vector of K is longer than the distance between the tip ends of the two vectors of M and C. That is, in the above prior-art scheme, the screen vectors of the three colors of M, C, and K do not form an closed triangle. When the screen vectors of three colors do not form an closed triangle as described above, by synthesizing screens for the three colors, components of the vectors that lie off the triangles (referred to as remainder components) cause low-frequency moiré in which a rosette pattern repeatedly appears with low-frequency periodicity and slightly changed appearance. FIG. 5 shows an M-C-K rosette pattern corresponding to the screen set of FIG. 2 in (6), and FIG. 8 shows an M-C-K rosette pattern corresponding to the screen set of FIG. 6 in (4) of (b).
Regarding the problem associated with such three color synthesis, Japanese Patent Laid-Open Publication No. Hei 05-257268 (corresponding to U.S. Pat. No. 5,155,599) and Japanese Patent Laid-Open Publication No. 2000-050071 disclose that the low-frequency moiré from the remainder components of the screen vectors among the three colors can be reduced by arranging the screen vectors so as to form a closed triangle formed by three colors. Basis vectors of a screen set according to a scheme described in the patent documents noted above are shown in FIG. 10, while screen vectors of the basis vectors are shown in FIG. 11. The screen set of this example has a resolution of 2400 dpi and approximately 170-190 lpi. According to this scheme, the screen vectors of the three colors of M, C, and K form closed triangles as shown in FIG. 12 and produce no remainder of vector components extended off the triangles. Dot pattern examples of the screen set are shown in FIG. 13A and moiré patterns of the superimposed screens are shown in FIG. 13B. With this scheme, as shown in FIG. 13B, moiré formed by superimposing of the screens is of a high frequency and noticeable low-frequency moiré does not emerge.
Related technologies for color reproduction using orthogonal halftone dot screens are described above. On the other hand, in a technical field of digital halftones, use of a non-orthogonal halftone screen for monochromatic tone reproduction as a technique of implementing flexible halftone dot patterns has been suggested (refer to U.S. Pat. No. 4,185,304 and “An Optimum Algorithm for Halftone Generation for Displays and Hard Copies” by Thomas M. Holladay, Proceedings of the SID, Vol.21/2, 1980, 185-192).
The schemes described in Japanese Patent Laid-Open Publication No. Hei 05-257268 and No. 2000-050071 are specifically targeted at three-color halftone printing, and any attempt to extend the three-color scheme to four-color halftone printing raises a problem regarding placement of the fourth color. Regarding the placement of the fourth-color screen, the above-listed patent documents provide no description. For the placement of the forth color, for example, schemes (i) in which Y and K are allocated to the same screen angle and (ii) in which Y is arranged at a middle screen angle between the screen angles of M and C are used. However, in scheme (i), the halftone patterns of Y and K become exactly the same, which poses remarkable hue change due to registration error of two colors of Y and K. On the other hand, scheme (ii) is equivalent to the scheme of FIG. 2, and thereby suffers from noticeable secondary color moiré of R and G containing color Y.
In U.S. Pat. No. 4,185,304 and in the Holladay reference, halftone design using a non-orthogonal screen for a monochromatic image is merely alluded to, and application of the non-orthogonal screens to a color image is not even suggested anywhere in the above documents. The utilization of the non-orthogonal screen brings about increased flexibility in screen angle design, but also leads to emergence of a secondary spectrum generated by the sum or the difference of two primary spectra at a band close to frequency components of the primary spectra. Accordingly, even screen design with reduced low-frequency moiré between primary spectra cannot completely prevent the emergence of low-frequency moiré due to components of secondary spectra. An effective non-orthogonal screen set has not yet been developed.